Proposal of a Score Based Approach to Sampling Using Monte Carlo Estimation of Score and Oracle Access to Target Density

TL;DR

This paper introduces a Monte Carlo-based method for sampling from a target density using only oracle access to the log likelihood and its gradient, avoiding the need for initial samples or neural network estimators.

Contribution

It proposes a novel Monte Carlo approach to estimate the score function directly from oracle access, enabling sampling without initial samples or black-box models.

Findings

Effective score estimation from oracle access

Sample generation via backward flow SDE without initial samples

Applicable to Bayesian and non-convex optimization problems

Abstract

Score based approaches to sampling have shown much success as a generative algorithm to produce new samples from a target density given a pool of initial samples. In this work, we consider if we have no initial samples from the target density, but rather $0^{th}$ and $1^{st}$ order oracle access to the log likelihood. Such problems may arise in Bayesian posterior sampling, or in approximate minimization of non-convex functions. Using this knowledge alone, we propose a Monte Carlo method to estimate the score empirically as a particular expectation of a random variable. Using this estimator, we can then run a discrete version of the backward flow SDE to produce samples from the target density. This approach has the benefit of not relying on a pool of initial samples from the target density, and it does not rely on a neural network or other black box model to estimate the score.